The Reds travelled to the KCOM Stadium off the back of an encouraging battling 1-1 draw with Premier League leaders Chelsea in mid-week, a result which ended a run of three straight defeats.
But familiar failings cost Liverpool as they suffered a fifth defeat in all competitions in 2017 alone, having lost just twice all season prior to 11 January.
Simon Mignolet spilled a Harry Maguire header for Hull's January addition Alfred N'Diaye to fire into an empty net before on-loan Everton striker Oumar Niasse made sure of victory late on.
That means Liverpool's place in the top-four is in jeopardy, with only a Swansea City win at the Etihad Stadium on Sunday enough to prevent Manchester City leapfrogging the Merseyside club into fourth.
And Klopp acknowledged that his team were way below standard on Humberside.
Klopp admits Reds 'show more' than they did in dismal Hull defeat
He admitted in his post-match press conference: "I've done four or five TV interviews, three or four radio interviews and usually after half-an-hour you feel better because you have no time to think about a lot of things after the game and then you immediately start answering questions. But this time, it doesn't feel better."
In his assessment of what went wrong for his Liverpool team, Klopp declared that they "gave easy goals away" and "didn't play the first-half as we should have played" compared to their second-half showing.
"You think then if we'd played from the beginning like this, with this direction, speed, kind of greed and all that stuff, then I think it would have been more difficult for Hull to cope with," the German continued.
He said that Liverpool "gave the first-half away" and in context of the result "gave the second-half away", explaining they "put ourselves under pressure in the second-half" after such a poor first 45 minutes.
Klopp acknowledged that the visitors "had the chances" but said that "good goalkeeper saves, passion and defending from Hull in the 18-yard box and the six-yard box with a leg here, a leg there, a block here" denied Liverpool.
He lamented that they conceded a second by giving away "an easy counter-attack again" and admitted: "We have to take all of the criticism."
Klopp said: "Not even a week ago in the press conferences, I spoke about expectations at Liverpool and said, 'Come on, it's allowed to have a positive look on the situation. We are still fourth in the league' and everything like this. After a game like this, it's not allowed to say something like that."
Klopp said that Liverpool "expect more from ourselves" and that they need to "show more than we did today", again accepting it as his "responsibility" to "make it possible for the players to show more."
He spoke of a "few things" and "little explanations" for their sub-par performance, suggesting Liverpool suffered from "a lack of rhythm in a few players" and "all that stuff."
Klopp believes the second-half "looked much more like it should do" but declared football "under pressure" is "difficult", as was trying to get through Hull when they "defend with a lot of legs in the box."
Yet he also said that the Tigers are "not only a defending team" and praised them for the way "they played football" and "were able to" because "there were spaces" when Liverpool "won the ball."
He continued: "We had these few moments [in the final third] but not in the right mood [to take advantage], especially in the first-half. That's difficult to accept."
Reds boss: We have to show we can qualify for the Champions League
Klopp was asked about whether recent results have affected the Reds' targets, with the latest weekend's round of results putting Liverpool a colossal 13 points behind Chelsea with 14 games left to play but declared there are other priorities to focus on.
He responded: "That's not my biggest problem. I want to play much better football with my team. It's not about where you want to be. You have to show what you should reach in a season."
Klopp said Liverpool "showed it a few times" but acknowledged "obviously" it was "long ago" that they "showed it consistently", calling it the first thing of all that his team "have to change, immediately."
He admitted that they "need to show much more consistency" than they currently do "on the positive side" and said Champions League qualification remains an "outstandingly big, big, big target" because "so many teams want to play" in what he called a "fantastic" competition.
Klopp says there are "so many challenges" which make it "outstandingly difficult" to qualify for the Champions League in England but said after the performance against Hull they "don't have to talk about this."
"We have to show now, really, that we are really ready to go for everything," insisted Klopp, who added that him saying as such will "not change a lot" and that the club "have to show it together."
He told reporters he will watch back their defeat to Hull to "understand it better", "especially the first-half and what happened there."
The Reds boss suggested that both of Hull's goals "really looked like presents" in how they "created the corner" for the first goal and then "of course the counter-attack for the second goal" which he said "was not too nice to watch."
He said that there are still "a lot of things to do" to improve as a unit and warned that "as an overall statement" Liverpool "have to change immediately" to get out of their current rut.
Record - weaker teams not a mentality problem, insists Klopp
But Klopp dismissed any suggestion that their attitude, or any complacency, was an issue - reiterating that he will "watch the game again" to "understand more what was the reason."
He noted that it isn't "the first time in the season" that Liverpool have heaped pressure on themselves, meaning that they had to "react" after the restart.
Klopp felt his team "showed the reaction" at Hull to "put them under pressure" but said that even if they would have won the game 2-1, he would still "100 per-cent" be "angry" about their first-half display.
He said that he has told the media a few times how he is "really interested" in performances because "you can build on performance" and improve.
"This week we had a really good performance [vs Chelsea] but obviously we didn't build on it," Klopp admitted. "So we will, and have to, take all the criticism from everywhere. We have to change it immediately."
And Klopp doesn't believe that this defeat necessarily indicates any struggle against teams lower down the league table, though he noted that he can "understand" if it "looks so from [the] outside" given their record "against these teams" and "the record against the other [top six] teams."
But he said that the players didn't "show anything of this" during the week, in defence of their mentality towards games against 'weaker' opposition, insisting that they "produce our problems most of the time by ourselves" rather than downplaying whoever they are facing.
"Our mistakes, my mistake, whoever; we have to show that it's not like this," vowed Klopp. "In a few days we have another opportunity and we can show then that we are ready for all the other games because it's [against] Tottenham who are a top team in the league. I think it would make sense to play our best in this game and then we have to prove the other thing later in the season."